Nonstationary shape estimation in electrical impedance tomography using a parametric level set-based extended Kalman filter approach

This paper presents a parametric level set based reconstruction method for non-stationary applications using electrical impedance tomography (EIT). Owing to relatively low signal to noise ratios in EIT measurement systems and the diffusive nature of EIT, reconstructed images often suffer from low spatial resolution. In addressing these challenges, we propose a computationally efficient shape-estimation approach where the conductivity distribution to be reconstructed is assumed to be piecewise constant, and the region boundaries are assumed to be non-stationary in the sense that the characteristics of region boundaries change during measurement time. The EIT inverse problem is formulated as a state estimation problem in which the system is modeled with a state equation and an observation equation. Given the temporal evolution model of the boundaries and observation model, the objective is to estimate a sequence of states for the nonstationary region boundaries. The implementation of the approach is based on the finite element method and a parametric representation of the region boundaries using level set functions. The performance of the proposed approach is evaluated with simulated examples of thorax imaging, using noisy synthetic data and experimental data from a laboratory setting. In addition, robustness studies of the approach w.r.t the modeling errors caused by inaccurately known boundary shape, non-homogeneous background and varying conductivity values of the targets are carried out and it is found that the proposed approach tolerates such kind of modeling errors, leading to good reconstructions in non-stationary situations

Damage tomography as a state estimation problem : crack detection using conductive area sensors

Typically, structural damage tomography (SDT) approaches aim to reconstruct a parameter field containing damage information from distributed data by solving an iterative inverse problem. Often, there are two shortcomings in adopting such an approach: (a) the high computational expense and (b) temporal information is inadequately used. In principle, both issues may be alleviated by approaching SDT as a state-estimation problem – i.e. treating the reconstruction problem as a temporally-evolving stochastic process. In this letter, we study the feasibility of state estimates in SDT. For this, we use an extended Kalman filter (EKF) for electrical resistance tomography (ERT) imaging of progressive cracking on an experimentally-tested reinforced concrete beam with an applied surface area sensing skin. In the investigation, we quantitatively analyze the effect of including multiple temporal data sets and corroborate EKF-ERT reconstructions with standard and advanced ERT approaches. It is shown that increasing the amount of temporal data significantly improves the quality of EKF-ERT reconstructions, which compare favorably with the standard and advanced ERT approaches. In addition, for the data sets used herein, the EKF-ERT regime computed seven reconstructions approximately 50-100 times faster than the standard and stacked approaches required to reconstruct one image, respectively

Performance Guarantee of a Class of Continuous LPV System with Restricted-Model-Based Control

This paper considers the problem of the robust stabilisation of a class of continuous Linear Parameter Varying (LPV) systems under specifications. In order to guarantee the stabilisation of the plant with very large parameter uncertainties or variations, an output derivative estimation controller is considered. The design of such controller that guarantee desired  induced gain performance is examined. Furthermore, a simple procedure for achieving the  norm performance is proved for any all-poles single-input/single-output second order plant. The proof of stability is based on the polytopic representation of the closed loop under Lyapunov conditions and system transformations. Finally, the effectiveness of the proposed method is verified via a numerical example

Parametric Level-sets Enhanced To Improve Reconstruction (PaLEnTIR)

In this paper, we consider the restoration and reconstruction of piecewise constant objects in two and three dimensions using PaLEnTIR, a significantly enhanced Parametric level set (PaLS) model relative to the current state-of-the-art. The primary contribution of this paper is a new PaLS formulation which requires only a single level set function to recover a scene with piecewise constant objects possessing multiple unknown contrasts. Our model offers distinct advantages over current approaches to the multi-contrast, multi-object problem, all of which require multiple level sets and explicit estimation of the contrast magnitudes. Given upper and lower bounds on the contrast, our approach is able to recover objects with any distribution of contrasts and eliminates the need to know either the number of contrasts in a given scene or their values. We provide an iterative process for finding these space-varying contrast limits. Relative to most PaLS methods which employ radial basis functions (RBFs), our model makes use of non-isotropic basis functions, thereby expanding the class of shapes that a PaLS model of a given complexity can approximate. Finally, PaLEnTIR improves the conditioning of the Jacobian matrix required as part of the parameter identification process and consequently accelerates the optimization methods by controlling the magnitude of the PaLS expansion coefficients, fixing the centers of the basis functions, and the uniqueness of parametric to image mappings provided by the new parameterization. We demonstrate the performance of the new approach using both 2D and 3D variants of X-ray computed tomography, diffuse optical tomography (DOT), denoising, deconvolution problems. Application to experimental sparse CT data and simulated data with different types of noise are performed to further validate the proposed method.Comment: 31 pages, 56 figure

Advances of deep learning in electrical impedance tomography image reconstruction

Electrical impedance tomography (EIT) has been widely used in biomedical research because of its advantages of real-time imaging and nature of being non-invasive and radiation-free. Additionally, it can reconstruct the distribution or changes in electrical properties in the sensing area. Recently, with the significant advancements in the use of deep learning in intelligent medical imaging, EIT image reconstruction based on deep learning has received considerable attention. This study introduces the basic principles of EIT and summarizes the application progress of deep learning in EIT image reconstruction with regards to three aspects: a single network reconstruction, deep learning combined with traditional algorithm reconstruction, and multiple network hybrid reconstruction. In future, optimizing the datasets may be the main challenge in applying deep learning for EIT image reconstruction. Adopting a better network structure, focusing on the joint reconstruction of EIT and traditional algorithms, and using multimodal deep learning-based EIT may be the solution to existing problems. In general, deep learning offers a fresh approach for improving the performance of EIT image reconstruction and could be the foundation for building an intelligent integrated EIT diagnostic system in the future

Efficient multiscale imaging of subsurface resistivity with uncertainty quantification using ensemble Kalman inversion

Electrical resistivity tomography (ERT) is widely used to image the Earth's subsurface and has proven to be an extremely useful tool in application to hydrological problems. Conventional smoothness-constrained inversion of ERT data is efficient and robust, and consequently very popular. However, it does not resolve well sharp interfaces of a resistivity field and tends to reduce and smooth resistivity variations. These issues can be problematic in a range of hydrological or near-surface studies, for example mapping regolith-bedrock interfaces. While fully Bayesian approaches, such as those using Markov chain Monte Carlo sampling, can address the above issues, their very high computation cost makes them impractical for many applications. Ensemble Kalman inversion (EKI) offers a computationally efficient alternative by approximating the Bayesian posterior distribution in a derivative-free manner, which means only a relatively small number of 'black-box' model runs are required. Although common limitations for ensemble Kalman filter-type methods apply to EKI, it is both efficient and generally captures uncertainty patterns correctly. We propose the use of a new EKI-based framework for ERT which estimates a resistivity model and its uncertainty at a modest computational cost. Our EKI framework uses a level-set parametrization of the unknown resistivity to allow efficient estimation of discontinuous resistivity fields. Instead of estimating level-set parameters directly, we introduce a second step to characterize the spatial variability of the resistivity field and infer length scale hyperparameters directly. We demonstrate these features by applying the method to a series of synthetic and field examples. We also benchmark our results by comparing them to those obtained from standard smoothness-constrained inversion. Resultant resistivity images from EKI successfully capture arbitrarily shaped interfaces between resistivity zones and the inverted resistivities are close to the true values in synthetic cases. We highlight its readiness and applicability to similar problems in geophysics